• Publications
  • Influence
A rack, which is the algebraic distillation of two of the Reidemeister moves, is a set with a binary operation such that right multiplication is an automorphism. Any codimension two link has aExpand
  • 443
  • 40
The braid-permutation group
Abstract We consider the subgroup of the automorphism group of the free group generated by the braid group and the permutation group. This is proved to be the same as the subgroup of automorphisms ofExpand
  • 154
  • 16
A Geometric Approach to Homology Theory
1. Homotopy functors 2. Mock bundles 3. Coefficients 4. Geometric theories 5. Equivariant theories and operations 6. Sheaves 7. The geometry of CW complexes.
  • 115
  • 14
Trunks and classifying spaces
Trunks are objects loosely analogous to categories. Like a category, a trunk has vertices and edges (analogous to objects and morphisms), but instead of composition (which can be regarded as given byExpand
  • 170
  • 13
On Kirby's calculus of links
(Receiued in revised form 21 July 1978) 4 FRAMED OR labelled link in S3 is a finite collection L of embedded circles in S’, each one of which is labelled by an integer. In [3] and [7] Lickorish andExpand
  • 135
  • 10
Ordering the braid groups
We give an explicit geometric argument that Artin’s braid group Bn is rightorderable. The construction is elementary, natural, and leads to a new, effectively computable, canonical form for braidsExpand
  • 93
  • 7
  • PDF
The compression theorem I
This the first of a set of three papers about the Compression Theorem: if M^m is embedded in Q^q X R with a normal vector field and if q-m > 0, then the given vector field can be straightened (ie,Expand
  • 57
  • 7
  • PDF
Given a characteristic class on a locally ordered combinatorial manifold M there exists a cocycle which represents the class on M and is locally defined, i.e. its value on a E M depends only on theExpand
  • 24
  • 6
  • PDF
The rack space
The main result of this paper is a new classification theorem for links (smooth embeddings in codimension 2). The classifying space is the rack space and the classifying bundle is the first JamesExpand
  • 67
  • 4
  • PDF
An Introduction to Species and the Rack Space
Racks were introduced in [FR]. In this paper we define a natural category like object, called a species.* A particularly important species is associated with a rack. A species has a nerve, analogousExpand
  • 66
  • 3